A micromechanical pressure sensor is described in published German patent document DE 103 23 559, which pressure sensor is based on the piezoresistive transducer principle for converting a mechanical force into an electrical signal. A conventional design of a micromechanical pressure sensor having piezoresistive transducer elements is illustrated in FIG. 1, in which design a substrate having an anodically etched diaphragm is anodically bonded to glass. Furthermore, published German patent document DE 100 32 579 discusses manufacturing the diaphragm and a cavity situated behind the diaphragm from porous silicon, which type of a sensor design is illustrated in FIG. 2. The chip is glued to a ceramic or into a pre-mold housing, and for protection against environmental influences it is passivated using gel which is held on the chip via a gel ring. A disadvantage of the passivation using gel is that gas, in particular under high pressure, is diffused into the gel. When the dissolved gas returns to the gaseous state, e.g., as the result of a pressure drop, the bonding wires running through the gel which produce the contact to the chip may be destroyed.